Алгоритмы цифровой обработки данных измерений, обеспечивающие угловое сверхразрешение

Abstract

Incorrect one- and two-dimensional inverse problems of reconstructing images of objects with angular resolutionexceeding the Rayleigh criterion are considered. The technique is based on the solution of inverse problems of source reconstruction signals described Fredholm integral equations. Algebraic methods and algorithms for processing dataobtained by measuring systems in order to achieve angular superresolution are presented. Angular superresolution allows you to detail images of objects, solve problems of their recognition and identification on this basis. The efficiency of using algorithms based on developed algebraic methods and their modifications in parameterization the inverse problems under study and further reconstructing approximate images of objects of various types is shown. It is shown that the noise immunity of the obtained solutions exceeds many known approaches. The results of numerical experiments demonstrate the possibility of obtaining images with a resolution exceeding the Rayleigh criterion by 2-6 times at small values of the signal-to-noise ratio. The ways of further increasing the degree of superresolution based on the intelligent analysis of measurement data are described. On the basis of the preliminary information on a source of signals algorithms allow to increase consistently the effective angular resolution before achievement greatest possible for a solved problem. Algorithms of secondary processing of the information necessary for it are described. It is found that the proposed symmetrization algorithm improves the quality of solutions to the inverse problems under consideration and their stability. The examples demonstrate the successful application of modified algebraic methods and algorithms for obtaining images of the objects under study in the presence of a priori information about the solution. The results of numerical studies show that the presented methods of digital processing of received signals allow us to restore the angular coordinates of individual objects under study and their elements with super-resolution with good accuracy. The adequacy and stability of the solutions were verified by conducting numerical experiments on a mathematical model. It was shown that the stability of solutions, especially at a significant level of random components, is higher than that of many other methods. The limiting possibilities of increasing the effective angular resolution and the accuracy of image reconstruction of signal sources, depending on the level of random components in the data utilized, are found. The effective angular resolution achieved in this case is 2—10 times higher than the Rayleigh criterion. The minimum required signal-to-noise ratio for obtaining adequate solutions with super-resolution is 13—16 dB for the described methods, which is significantly less than for the known methods. The relative simplicity of the presented methods allows you to use inexpensive computing devices and work in real time.